Question: Solve for $x$ : $x^2 - 6x - 27 = 0$
The coefficient on the $x$ term is $-6$ and the constant term is $-27$ , so we need to find two numbers that add up to $-6$ and multiply to $-27$ The two numbers $-9$ and $3$ satisfy both conditions: $ {-9} + {3} = {-6} $ $ {-9} \times {3} = {-27} $ $(x {-9}) (x + {3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -9) (x + 3) = 0$ $x - 9 = 0$ or $x + 3 = 0$ Thus, $x = 9$ and $x = -3$ are the solutions.